1. Field of the Invention
The present invention relates generally to a method for measuring the flow rate of fluids and, more particularly, to a method for measuring the flow rate of a component of a two-component fluid mixture.
2. Brief Description of the Prior Art
In industrial processes involving fluids which are considered to be two-component fluid mixtures, a need exists to accurately measure the concentration of one of the components of the two-component fluid mixture. Typically a two-component fluid mixture consists of either a solid component fully or partially dissolved within a liquid carrier fluid, or a liquid component mixed with a liquid carrier fluid. In addition to measuring the concentration of one of the components of the two-component mixture, a need exists to accurately measure the flow rate corresponding to the measured component.
In the beverage industry, for example, there is a need to accurately measure and control the concentration of sugar in water and to determine the associated total amount of sugar used. In the pulp and paper industry, knowledge of the concentration of TiO.sub.2 and its associated flow rate is valuable in accurately controlling paper coating processes. Similarly, in oil production, there is a need to accurately measure the oil and water concentrations and determine the associated oil production rates for royalty calculation purposes.
There are several known prior art methods of measuring the flow rate and/or the concentration of a component of a two-component fluid mixture. One of these methods is described in U.S. Pat. No. 4,689,989 to Aslesen et al. This method is also described in "EXAC Mass Flow Meter Applications Manual (8300 EX, 8310 EX)", pages 2-14 to 2-16.
The method described in these publications is based on the fact that, at a known temperature, a determinable relationship between the density of a two-component mixture and the concentration of one of the components of that mixture exists.
The relationship between the density of the two-component mixture and the concentration of one of the components of that mixture can be plotted graphically as is illustrated by curve 10 in FIG. 1 of the accompanying drawings. In this figure, the density .rho. of the two-component mixture is plotted on the vertical axis 12 and the concentration C of one of the components of that mixture is plotted on the horizontal axis 14.
One method of determining the density concentration curve 10 is to create a mixture in which the concentration of one of the components is known. The sample is then heated to a known temperature and its density is measured. If the known component concentration, say C.sub.1 and the measured density, say .rho..sub.1, are plotted on the vertical and horizontal axes 12 and 14, respectively, a point (C.sub.1 ; .rho..sub.1) is defined in the C-.rho. plane between the axes 12 and 14.
The above step is then repeated by producing a different sample of the mixture with a different component concentration, say C.sub.2, and its measuring density, say .rho..sub.2, at the same temperature at which the first concentration C.sub.1 and density .rho..sub.1 values were measured. This second measurement will yield a further point (C.sub.2 ; .rho..sub.2) in the C-.rho. plane.
The above process is repeated until sufficient points (typically 15) have been determined to plot the curve 10.
Once this curve has been determined, it can be used to measure the concentration of a component of a two-component fluid mixture. The way this is done is by first measuring the density of a two-component fluid mixture. Typically, this density of the fluid mixture can be measured by using devices such as a pycnometer, a vibrating tube densitometer, gamma ray density gauges, hygrometers, or any other suitable apparatus or technique. This measured density is then plotted on the vertical axis 12, read across to curve 10 and, from curve 10, down to determine the concentration value from the horizontal concentration axis 14.
A major problem with this method is that the curve 10 is derived at a single known temperature and can only be used to determine concentrations in a mixture at that temperature. If this curve 10 is used to determine the concentration of the component of a two-component fluid mixture which is at a different temperature to which the curve 10 was produced, erroneous results will occur.
This can be illustrated by considering the following hypothetical situation: If the density of a two-component fluid mixture is .rho..sub.1, the concentration of the measured component of the two-component fluid will, according to curve 10, be equal to C.sub.1. This is true, as is described above, only if the temperature of the fluid under consideration is the same as that for which a curve 10 is derived. If that same fluid is now heated to a greater temperature, its density would decrease to a value, say .rho..sub.3. If we use curve 10 to determine the concentration of the component of the mixture, this will yield a concentration C.sub.3. However, this concentration C.sub.3 is clearly incorrect because the concentration of the component has not changed and is still at a value C.sub.1.
This is because concentration, on either a mass or a weight basis, does not change with the temperature of the fluid, even though the fluid's density does. Concentration on a mass basis is simply proportional to the ratio of the concentrate mass divided by the sum of the concentrate mass plus the carrier mass. Mass does not change with temperature and, therefore, neither does concentration on a mass basis. However, density, which defined as mass per volume, does change with temperature since volume typically increases with increasing temperature.
In fact, with the change in density with the change in temperature, a change in the density-concentration relationship has occurred. This changed relationship is indicated by the broken-line curve 16 in FIG. 1 which is drawn through the intersection point between a vertical line drawn up from concentration C.sub.1 and the horizontal line drawn from density .rho..sub.3. What this second curve 16 illustrates is that, for an accurate concentration determination at the second temperature a different curve (in this case curve 16) should be used.
A seemingly straightforward solution to this problem would be to accurately account for temperature changes. One way of doing this would be to make allowance for the changes in a fluid's density based on its coefficient of thermal expansion. However, a mixture of two components cannot accurately be characterized as having a single, constant coefficient of thermal expansion because the two components will behave differently as temperature changes and will depend on the relative amendment of the two components present which, of course are a priori, unknown. This is primarily because each component of the mixture will exhibit different rates of thermal expansion.
Furthermore, it is not always possible to know or obtain the expansion coefficient for each fluid component. For example, in the case of a sugar solution, one would have to know the expansion coefficient for both water (which is known) and that of sugar in solution (which is not known).
Another way of making allowances for changes in temperature would be to plot a large number of density-concentration curves over a large range of different temperature conditions. Unfortunately, this is not always practical to do for each and every type of solution that one would wish to measure. Furthermore, certain density-concentration measurements are required to be so accurate that temperature differences of only a few degrees Fahrenheit could lead to unacceptable inaccuracies. To produce a curve for each possible temperature range is similarly impractical.
For the above reasons, therefore, the prior art methods of determining density concentration relationships and, more particularly, the concentration of a component of a two-component fluid mixture and its associated flowrate are insufficient for providing for situations where the temperature of the mixture varies.